Properties

Conductor 2000
Order 100
Real no
Primitive no
Minimal no
Parity even
Orbit label 4000.cw

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4000)
 
sage: chi = H[41]
 
pari: [g,chi] = znchar(Mod(41,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2000
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 100
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4000.cw
Orbit index = 75

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4000}(41,\cdot)\) \(\chi_{4000}(121,\cdot)\) \(\chi_{4000}(281,\cdot)\) \(\chi_{4000}(361,\cdot)\) \(\chi_{4000}(441,\cdot)\) \(\chi_{4000}(521,\cdot)\) \(\chi_{4000}(681,\cdot)\) \(\chi_{4000}(761,\cdot)\) \(\chi_{4000}(841,\cdot)\) \(\chi_{4000}(921,\cdot)\) \(\chi_{4000}(1081,\cdot)\) \(\chi_{4000}(1161,\cdot)\) \(\chi_{4000}(1241,\cdot)\) \(\chi_{4000}(1321,\cdot)\) \(\chi_{4000}(1481,\cdot)\) \(\chi_{4000}(1561,\cdot)\) \(\chi_{4000}(1641,\cdot)\) \(\chi_{4000}(1721,\cdot)\) \(\chi_{4000}(1881,\cdot)\) \(\chi_{4000}(1961,\cdot)\) \(\chi_{4000}(2041,\cdot)\) \(\chi_{4000}(2121,\cdot)\) \(\chi_{4000}(2281,\cdot)\) \(\chi_{4000}(2361,\cdot)\) \(\chi_{4000}(2441,\cdot)\) \(\chi_{4000}(2521,\cdot)\) \(\chi_{4000}(2681,\cdot)\) \(\chi_{4000}(2761,\cdot)\) \(\chi_{4000}(2841,\cdot)\) \(\chi_{4000}(2921,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,-i,e\left(\frac{11}{25}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{33}{100}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{33}{50}\right)\)\(e\left(\frac{19}{100}\right)\)\(e\left(\frac{41}{100}\right)\)\(e\left(\frac{3}{25}\right)\)\(e\left(\frac{17}{100}\right)\)\(e\left(\frac{23}{100}\right)\)\(e\left(\frac{7}{50}\right)\)\(e\left(\frac{99}{100}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{100})\)